Cloth simulated hair inside of an Armature?
There should be no problem with such setup. Follow this to make sure everything is fine:


Mesh is bind to the armature with weight paint:



Here the whole plane is fully weighted to the bone.
Create a new vertex group for pinning. Here I pinned 2 corner vertices:


Use this pinning group for cloth simulation. Also make sure the cloth simulation is after armature deform in modifiers so it takes as input the posed mesh:




Now the simulation works on top of armature as expected: